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 By: JessicaTan (offline)  Monday, July 22 2013 @ 04:30 AM CDT (Read 928 times)
JessicaTan

Answerkey : (a) 1.1L (b) 0.4L

Regular Member

Registered: 10/17/09
Posts: 82

 By: jo sarah (offline)  Monday, July 22 2013 @ 08:02 AM CDT
jo sarah

If you can understand the algebraic approach, here is it:

Let the volume of juice in A and B be a and b litres respectively.

Then, a + 1.3 = 1.6b
so that, 1.6b - a = 1.3.................[1]

and 1.8a = b + 0.48....................[3]
that is, 1.8a - b =0.48
which, if you multiply both sides by 1.6 gives:
2.88a - 1.6b = 0.768...................[2]

[1] + [2] gives:
1.88a = 2.068
therefore, a = 2.068/1.88 = 1.1

and from [3],
b = 1.8a - 0.48 = 1.5

so that, b - a = 1.5 - 1.1 = 0.4

thus, (a) volume of juice in A is 1.1 litres.
and (b) difference in volumes in A and B is 0.4 litre.

regards,
jo sarah

Regular Member

Registered: 03/20/12
Posts: 111

 By: echeewh (offline)  Monday, July 22 2013 @ 06:33 PM CDT
echeewh

Hey Jessica,

An alternative to the algebraic approach is as follows:

<if 1.3l / 1300 ml added to A>

A : B
16 : 10
8 : 5

<before>

A: 8p - 1300
B: 5p

<after 480 ml added to B>

A : B
10 : 18
5 : 9

A: 8p - 1300 = 5u
B: 5p + 480 = 9u

Rearranging these 2 equations ...

A: 8p - 5u = 1300 -- (1)
B: 9u - 5p = 480 -- (2)

To find the volumes in the bottles, eliminate (u).

(1)x9:
72p - 45u = 11700 -- (3)

(2)x5:
45u - 25p = 2400 -- (4)

(3)+(4):
72p - 25p = 11700 + 2400
47p = 14100
1p --> 14100 ÷ 47 = 300

(a)
Volume in A = 8p - 1300
8p - 1300 = (8 × 300) - 1300
= 2400 - 1300
= 1100 ml
= 1.1 l

(b)
B = 5p --> 5 × 300 = 1500 ml = 1.5 l

Difference in volume between both bottles
= 1.5 - 1.1
= 0.4 l

==========

Trust this helps.

Do let me know again if there's further clarification.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

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